Finite Group DatabasebetaFinite Group Databasebeta| order | 1680 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#10587938 |
| Hall | C3×C5×C7 ⋊ #41 |
| Hall | C5×C7 ⋊ C3×#41 |
| Hall | C3×C7 ⋊ #711 |
| Hall | C3×C5 ⋊ #1157 |
| Sylow | C7 ⋊ C3×#711 |
| Sylow | C5 ⋊ C3×#1157 |
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 840 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1680, 652);